How to animate 'Bridge Edge Loop' effect
The main issue I see with bridge edge loops and using a mesh for this, is that it will be very hard to control the deformation of the mesh as it moves It would require some rigging (bones and an IK system) to work correctly, in my opinion is too much trouble.

An alternative would be to use curves and hooks.



Here's a curve with some bevel. You can control the radius of each point separately.

 

To add hooks, select one of the control points, press the space bar and type hook, you''l get the option "hook to new object". That will create an empty. 
Do the same for the other segment of the curve and animate the movement of the empties.